Bruce A. Murtagh

Large-scale linearly constrained optimization

An algorithm for solving large-scale nonlinear programs with linear constraints is presented. The method combines efficient sparse-matrix techniques as in the revised simplex method with stable quasi-Newton methods for handling the nonlinearities. A general-purpose production code (MINOS) is described, along with computational experience on a wide variety of problems.

Interactive fuzzy programming with preference criteria in multiobjective preference criteria in multiobjective decision-making

Abstract This paper presents a methodology for solving a decision-making problem involving a multiplicity of objectives as well as of selection criteria for the best-compromise solution. The concept of fuzzy sets is utilized in such a way that the decision-maker can vary interactively the fuzzy membership values which are functions of the decision-makers input information known as preference criteria. A fuzzy cardinal priority ranking of the generated nondominated solutions can be determined to provide a useful decision-making aid.

A heuristic procedure for solving the quadratic assignment problem

Abstract An heuristic approach to the solution of the quadratic assignment problem is presented. A simple procedure is used to get a good feasible starting point, then the problem is solved as a nonlinear program (ignoring the integrality conditions) using MINOS, and lastly the near integer solution is converted into an integer feasible solution using an heuristic procedure. The results compare favourably with other procedures in the literature. A superior solution to the 19 × 19 hospital layout problem is found.

SUBGRADIENT OPTIMIZATION APPLIED TO A DISCRETE NONLINEAR PROBLEM IN ENGINEERING DESIGN

The particular application considered here is the design of relief-header systems, involving compressible fluid flow through tree-networks. The flowrates are specified, and the design problem involves the choice of discrete pipe sizes to minimize total cost while satisfying pressure-drop constraints, which are highly nonlinear.The problem is solved in two stages. Firstly the problem of obtaining the optimal set of continuous pipe sizes is addressed; it turns out that a dual formulation provides and extremely rapid solution. Next, a subgradient optimization procedure is used on the dual in order to solve for the discrete pipe sizes. Networks of up to 78 paths and 205 sections, each involving 50 discrete pipe sizes, have been solved.

Interactive group decision-making using fuzzy programming with preference criteria

Abstract This paper presents an algorithm for solving a decision situation involving many decision-makers who are all concerned with determining a compromise solution to a given multiobjective problem. Fuzzy programming enables the decision-makers to vary, at any given iteration in the execution of a computer programme, their fuzzy aspiration levels in terms of input information known as preference criteria and underachievement tolerance values. Since conflict in aspiration levels usually entails an infeasible situation, a binary search technique is applied to the set of aspiration levels until a feasible efficient and acceptable compromise solution is obtained.

A Markovian process in interactive multiobjective decision-making

Abstract This paper presents a linear programming approach that will provide a means of ranking nondominated solutions of a multiobjective decision problem. The proposed approach can also be used to generate additional nondominated solutions. The variable preferences of a decision-maker with respect to a set of nondominated solutions can be analyzed as a Markovian process with an infinite number of stages and a finite number of decision states.